Challenging Probability problem 2

Problem

Vegetarian club consists of 2 married couples and 8 singles. The club is to select a delegation of 4 members to participate in an overseas conference. Find the probability that the delegation contains exactly one married couple.

Answer: 8/45

Solution

Case 1: 1 couple + 1 of the other couple + 1 single

(2 couples choose 1 couple) X (2 choose 1 from the other couple) X (8 singles choose 1) = 32

Case 2: 1 couple and 2 singles

(2 couples choose 1 couple) X (8 singles choose 2) = 56

No restrictions  = 12 C 4 = 495

Probability = (32+56) / 495 = 8/45

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